Finite Group Databasebeta

← #11869700

Subgroups — #11869700

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595005C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic, complemented
3#10592436C211yesmaximal, characteristic, complemented
4C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×#4723C211yesmaximal, characteristic, complemented
6#10591136C211yesmaximal, characteristic, complemented
7#10591127C211yesmaximal, characteristic, complemented
8#10590707C211yesmaximal, characteristic, complemented
9#10590706C211yesmaximal, characteristic, complemented
10#10590690C211yesmaximal, characteristic, complemented
11#10590690C211yesmaximal, characteristic, complemented
12#10590682C211yesmaximal, characteristic, complemented
13#10590679C211yesmaximal, characteristic, complemented
14#10590677C211yesmaximal, characteristic, complemented
15#10590675C211yesmaximal, characteristic, complemented
16#81515—31nomaximal
17#78591—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64139C2211yescharacteristic
21#64135C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26#63977—21no—
27D3×#217—21no—
28#63955—21no—
29#63952—21no—
30#63909C2211yescharacteristic
31#63904—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34C4×D3×Dic3—21no—
35#63856C2211yescharacteristic
36#63855—21no—
37#63850—21no—
38#63841C2211yescharacteristic
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic
41C32×C22⋊C8C2211yescharacteristic
42#63648C2211yescharacteristic, complemented
43#63648C2211yescharacteristic, complemented
44#63645C2211yescharacteristic, complemented
45#63644C2211yescharacteristic, complemented
46C3×#830C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#5791—31no—
62C2×#926—31no—
63#5627—31no—
64D3×#117—31no—
65C3×#485—31no—
66C2×C3×C22⋊C8—31no—
67#5113—31no—
68#5113—31no—
69#5106—31no—
70#5106—31no—
71#5045—31no—
72#5003—31no—
73#4882—31no—
74#4880—31no—
75#4863—31no—
76#4860—31no—
77#4811—31no—
78#4805—31no—
79#4804—31no—
80#4804—31no—
81#4737—31no—
82#4737—31no—
83#4737—31no—
84#4737—61no—
85#4736—31no—
86#4735—31no—
87D3×C22⋊C8D311yescharacteristic, complemented
88#4723—31no—
89#4723D311yescharacteristic, complemented
90#4722—31no—
91#4721—31no—
92C23×C3×D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C22×C3×Dic3D411yescharacteristic
97C2×C3×C4×D3—22no—
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3799—22no—
110#3799—22no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×D3×C8—22no—
129C3×D3×C8—22no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141#3091—91noSylow
142C23×C3×C4—31no—
143C2×#239—31no—
144C2×#235—31no—
145C22×C4×D3C2×D311yescharacteristic
146C22×C3×C8—31no—
147C22×C3×C8—31no—
148C3×C22⋊Q8—31no—
149C3×#117—31no—
150#953—61no—
151C2×#217—61no—
152#946—31no—
153#930—31no—
154#930—31no—
155#930—31no—
156#930—61no—
157#929—61no—
158C4×#67—61no—
159C4×#67—61no—
160#926—31no—
161#926—31no—
162#926—31no—
163#926—31no—
164#926—31no—
165#926—61no—
166#926—61no—
167#926—61no—
168#926C2×D311yescharacteristic
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171#924—31no—
172#924C2×D311yescharacteristic
173C2×C4×Dic3—61no—
174C2×D3×C8C2×D311yescharacteristic
175C2×D3×C8C2×D311yescharacteristic
176#895—31no—
177#894—61no—
178#893—61no—
179#892—31no—
180#892—31no—
181#892—31no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184#882—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187#877—61no—
188#872—61no—
189C42×D3—61no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×C22⋊C8—21no—
195C3×C22⋊C8—31no—
196C3×C22⋊C8—31no—
197C3×C22⋊C8—31no—
198C3×C22⋊C8C2×D311yescharacteristic
199C3×C22⋊C8C2×D311yescharacteristic
200#835—31no—
201#835—31no—
202#830C2×D311yescharacteristic
203#821—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#821—61no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212(C2×D3)⋊C8C2×D311yescharacteristic
213#818—31no—
214#818—31no—
215#818—31no—
216#818—31no—
217#818—61no—
218#818C2×D311yescharacteristic, complemented
219#817—31no—
220#817—31no—
221#817—31no—
222#817—31no—
223#817—61no—
224#817C2×D311yescharacteristic, complemented
225#816—31no—
226#816—31no—
227#816C2×D311yescharacteristic, complemented
228#816C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—22no—
238C22×C3×D3—22no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—22no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—22no—
263C3×C4×D3#4112yes—
264C3×C4×D3#4112yes—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#626—42no—
268#626—42no—
269#624—42no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—91no—
277C2×#117—91no—
278#485—31no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—91no—
289#416—91no—
290C2×C22⋊C8—31no—
291C24×C3—31no—
292C23×D3D1211yescharacteristic
293C2×C3×Q8—31no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—62no—
301C22×C3×C4—62no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—121no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3D1211yescharacteristic
312#239—62no—
313#239—62no—
314#235—62no—
315#235—62no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×C4×D3—22no—
322C2×C4×D3—22no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3D1211yescharacteristic
328C2×C4×D3D1211yescharacteristic
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—62no—
337C2×C3×C8—62no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—61no—
349#217—21no—
350#217—21no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—121no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—21no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D3×C8—22no—
399D3×C8—22no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—44no—
412C2×C3×D3#12312yes—
413C2×C3×D3#13512yes—
414C32×C4—21no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3#12312yes—
426C2×#41—91no—
427C23×C4—31no—
428C22×C8—31no—
429C22×C8—31no—
430#123—181no—
431C22⋊Q8—31no—
432C22⋊Q8—91no—
433#121—91no—
434#121—91no—
435#120—181no—
436C4×D4—181no—
437C4×D4—181no—
438#117—31no—
439#117—91no—
440#117—91no—
441#117—91no—
442#117—91no—
443#117—181no—
444#117—181no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C22⋊C4—181no—
448C2×C42—181no—
449#107—31no—
450#107—91no—
451#107—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457#103—31no—
458#103—31no—
459#103—91no—
460#103—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—31no—
467C22⋊C8—31no—
468C22⋊C8D3211yescharacteristic
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—62no—
473C23×C3—62no—
474C23×C3—121no—
475C23×C3C2×D1211yescharacteristic
476C23×C3D3×D411yescharacteristic
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—41no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—121no—
483C22×D3C2×D1211yescharacteristic
484C22×D3C2×D1211yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4C2×D1211yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—122no—
513#67—122no—
514#67—122no—
515#67—122no—
516#67—242no—
517C2×Dic3—22no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—122no—
532C2×Dic3—122no—
533C2×Dic3C2×D1211yescharacteristic
534C2×Dic3C2×D1211yescharacteristic
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12—121no—
541D12—122no—
542D12—122no—
543C4×D3—22no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—22no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3#23712yes—
552C4×D3#23712yes—
553Dic6—21no—
554Dic6—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—41no—
560C3×C8—41no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C2×C32—41no—
566C2×C32C2×#12311yescharacteristic
567C2×C32C2×#13511yescharacteristic
568C2×C32#57511yescharacteristic
569C3⋊D3—81no—
570C3×D3—22no—
571C3×D3—22no—
572C24—31no—
573#41—182no—
574#41—182no—
575C2×Q8—31no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4C2×D3211yescharacteristic
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—62no—
594C2×C8—62no—
595C2×C8C2×D3211yescharacteristic
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—61no—
617C42—181no—
618C42—181no—
619C42—181no—
620C42—181no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—32no—
629C22×C3—32no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—124no—
638C22×C3C22×D1211yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—44no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—241no—
654C2×D3#88612yes—
655C2×D3#90412yes—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—32no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C2×#23711yescharacteristic
668C3×C4C2×#23711yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—241no—
683Dic3—241no—
684Dic3—241no—
685Dic3#88612yes—
686C32#309111yescharacteristic, complemented, Sylow
687C23—31no—
688C23—31no—
689C23—62no—
690C23—62no—
691C23—121no—
692C23—181no—
693C23D3×D1211yescharacteristic
694Q8—61no—
695Q8—61no—
696D4—181no—
697D4—181no—
698D4—362no—
699D4—362no—
700D4—362no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—31no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—362no—
720C2×C4—362no—
721C2×C4—362no—
722C2×C4D3×D1211yescharacteristic
723C2×C4C22×D3211yescharacteristic
724C8—21no—
725C8—21no—
726C8—61no—
727C8—61no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—41no—
732C2×C3—41no—
733C2×C3—62no—
734C2×C3—62no—
735C2×C3—81no—
736C2×C3C2×#88611yescharacteristic
737C2×C3D3×#12311yescharacteristic
738C2×C3C2×#90411yescharacteristic
739C2×C3#574811yescharacteristic
740C2×C3D3×#13511yescharacteristic
741C2×C3#577711yescharacteristic
742D3—22no—
743D3—22no—
744D3—241no—
745D3—241no—
746D3—481no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—32no—
751C22—32no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—124no—
757C22—361no—
758C22—361no—
759C22—361no—
760C22C2×D3×D1211yescharacteristic
761C4—21no—
762C4—32no—
763C4—61no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—361no—
769C4—361no—
770C4—361no—
771C4D3×#23711yescharacteristic
772C4D3×#23711yescharacteristic
773C3—21no—
774C3#7859111yescharacteristic, complemented
775C3#8151511yescharacteristic, complemented
776C2—41no—
777C2—62no—
778C2—62no—
779C2—721no—
780C2D3×#88611yescharacteristic
781C2D3×#90411yescharacteristic
782C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595005C2
hypercenterC22⋊C8D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. D3×#926C2semidirect
3. #10592436C2semidirect
4. C3×D3×C22⋊C8C2semidirect
5. C3×#4723C2semidirect
6. #10591136C2semidirect
7. #10591127C2semidirect
8. #10590707C2semidirect
9. #10590706C2semidirect
10. #10590690C2semidirect
11. #10590690C2semidirect
12. #10590682C2semidirect
13. #10590679C2semidirect
14. #10590677C2semidirect
15. #10590675C2semidirect
42. #63648C22semidirect
43. #63648C22semidirect
44. #63645C22semidirect
45. #63644C22semidirect
49. C3×#818C22semidirect
50. C3×#817C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. #63575C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
87. D3×C22⋊C8D3semidirect
89. #4723D3semidirect
218. #818C2×D3semidirect
224. #817C2×D3semidirect
227. #816C2×D3semidirect
228. #816C2×D3semidirect
686. C32#3091semidirect
774. C3#78591semidirect
775. C3#81515semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105950052
D3×#9262
#105924362
C3×D3×C22⋊C82
C3×#47232
#105911362
#105911272
#105907072
#105907062
#105906902
#105906822
#105906792
#105906772
#105906752
#815153
#785913